The -binreg- routine fits generalized linear models for the
binomial family. It is presumably preferred over fitting the same
model in -glm-, not only for the convenience of not having to
specify the distributional family in the command line, but also
because in iteratively seeking the estimates it checks to make sure
that they are consistent with the range of allowable probabilities
(i.e. 0 to 1), as described on page 138 of the manual [Ref A-G].
So my question is, why does -binreg- appear to be so
bad at this checking?
Take a very simple model using the auto.dta.
. use "C:\Stata\auto.dta", clear
(1978 Automobile Data)
. binreg foreign mpg, rr
Residual df = 72 No. of obs = 74
Pearson X2 = 73.88014 Deviance = 78.99933
Dispersion = 1.026113 Dispersion = 1.097213
Bernoulli distribution, log link
----------------------------------------------------------------------
| EIM
foreign | Risk Ratio Std. Err. z P>|z| [95% Conf. Interval]
--------+-------------------------------------------------------------
mpg | 1.097213 .0109901 9.26 0.000 1.075883 1.118966
----------------------------------------------------------------------
. predict phat, mu
. sum phat
Variable | Obs Mean Std. Dev. Min Max
-------------+-----------------------------------------------------
phat | 74 .3008965 .22691 .1072727 1.580984
Clearly a predicted probability > 1.5 is not a good estimate. Did
I do something wrong? Or did -binreg- do something wrong? Or is
this simply another example of why linear models of the logit and
probit have dominated analysis of binary data for decades?
By the way, note that if I fit the exact same model using -glm-,
this same observation gets a predicted probability of 1.43, so
-binreg- actually seems to do worse.
--
Jay S. Kaufman, Ph.D
-----------------------------
email: [email protected]
-----------------------------
Department of Epidemiology
UNC School of Public Health
2104C McGavran-Greenberg Hall
Pittsboro Road, CB#7435
Chapel Hill, NC 27599-7435
phone: 919-966-7435
fax: 919-966-2089
-----------------------------
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